I want to show that the binomial distribution:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]P(m)=\frac{n!}{(n-m)!m!}p^m(1-p)^{n-m} [/tex]

using Stirling's formula:

[tex]n!=n^n e^{-n} \sqrt{2\pi n} [/tex]

reduces to the normal distribution:

[tex]P(m)=\frac{1}{\sqrt{2 \pi n}} \frac{1}{\sqrt{p(1-p)}}

exp[-\frac{1}{2}\frac{(m-np)^2}{np(1-p)}]

[/tex]

Unfortunately, I keep on getting an extra term linear in m-np:

[tex] exp[\frac{m-np}{2n}\frac{2p-1}{(1-p)p}][/tex]

This term is zero if p=1/2, but I want to show that the binomial distribution reduces to the normal distribution for any probablity p.

Has anyone else had this problem, as I'm sure this derivation is fairly common?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Binomial and normal distros

**Physics Forums | Science Articles, Homework Help, Discussion**